How to calculated weighted gain of antenna?

I have this test specification for testing antennas and it defines weighted gain as follows:

The weighted gain is calculated from the transfer function (S21) using only the gain values within the specified in-band frequencies. The average represents the nominal gain of the LNA assembly. The tolerance specifies the maximum difference between the average and the measured weighted gain of the DUT.

My question is, what exactly is the weighting function here? I have a VNA that performs an S21 measurement and produces a log magnitude graph (Hz vs. dB) with various points between the two frequencies which I also have.

Am I supposed to take the average of all these points in the band? Is this the weighted gain? If so, how does it make sense when it says to take the difference between the average and the measured weighted gain when the average is the weighted gain?

I'm not an antenna expert and everything I've looked up talks about just the normal gain antenna as being a function of directivity and efficiency, and it mentions nothing about a weighting. Usually when something is weighted, there's usually some weighting function specified...

If anyone could clarify, I'd greatly appreciate it.

I did not know this specification and I also think it must specify the weighting function or it is incomplete (Can you provide a link to the document?)

But I’m pretty sure it is meant to be a simple mean value: You must calculate the mean value of all S21 data points within a certain bandwidth.

Attention: It is not correct to build the mean value of the LOG values, instead you must convert your datapoints to non LOG values first.

The average is declared as the nominal gain of your amplifier, so it is different from the weighted gain of the S21 data points (mean value).

• I'm not sure what I'm supposed to convert to then. It says that the S21 calculates values between the frequencies but they're in dB which is gain. And it specifies that I must calculate the weighted gain using these gain values. So if this is wrong, what values should they be?
– Jake
Oct 3, 2018 at 12:29
• Ok, lets discuss this with a simple example: Frequencies in band are 2.4GHz, 2.44GHz and 2.48GHz with S21 values of 3dB, 6dB and 3dB. Gain factors would be 2, 4 and 2 then. weighted gain in band follows as 8/3=2.67=4.3dB. Oct 3, 2018 at 16:04
• Thanks for the clarification. I understand now that there's a conversion. The specification is something used internal to my company so I probably can't post it publicly. I was just confused by what this definition meant.
– Jake
Oct 3, 2018 at 18:43